Module: Statistics2

Defined in:
lib/statistics2.rb,
lib/statistics2/no_ext.rb,
lib/statistics2/version.rb,
ext/statistics2.c

Overview

Indicate that we should skip loading of the C extension.

Constant Summary collapse

SQ2PI = 
Math.sqrt(2 * Math::PI)
LOG_2PI =

Gamma function

Math.log(2 * Math::PI)
N = 
8
B0 = 
1.0
B1 = 
-1.0 / 2.0
B2 = 
1.0 / 6.0
B4 = 
-1.0 / 30.0
B6 = 
1.0 / 42.0
B8 = 
-1.0 / 30.0
B10 = 
5.0 / 66.0
B12 = 
-691.0 / 2730.0
B14 = 
7.0 / 6.0
B16 = 
-3617.0 / 510.0
NO_EXT = 
true
VERSION = 
0.54

Class Method Summary collapse

Class Method Details

.bin_x(n, p, x) ⇒ Object 



730
 
# File 'ext/statistics2.c', line 730

def bin_x(n, p, x); bindist(n, 1.0 - p, n - x);  end

.bindens(n, p, x) ⇒ Object

discrete distributions



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# File 'ext/statistics2.c', line 709

def bindens(n, p, x)
  p = p.to_f
  q = 1.0 - p
  combi(n, x) * p**x * q**(n - x)
end

.bindist(n, p, x) ⇒ Object 



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# File 'ext/statistics2.c', line 716

def bindist(n, p, x)
  (0..x).inject(0.0) do |s, k|
    s + bindens(n, p, k)
  end
end

.binX_(n, p, x) ⇒ Object

discrete distributions



596
 
# File 'lib/statistics2.rb', line 596

def binX_(n, p, x); bindist(n, p, x); end

.chi2_x(n, x) ⇒ Object

chi-square-distribution



521
 
# File 'lib/statistics2.rb', line 521

def chi2_x(n, x); 1.0 - chi2dist(n, x); end

.chi2dist(n, x) ⇒ Object

inverse of chi-square-distribution



233
 
# File 'lib/statistics2.rb', line 233

def chi2dist(n, x); 1.0 - q_chi2(n, x); end

.chi2X_(n, x) ⇒ Object

Returns the integral of Chi-squared distribution with n degrees of freedom over [0, x].



524
 
# File 'lib/statistics2.rb', line 524

def chi2X_(n, x); chi2dist(n, x); end

.f_x(n1, n2, x) ⇒ Object

Returns the integral of F-distribution with n1 and n2 degrees of freedom over [x, Infty).



577
 
# File 'lib/statistics2.rb', line 577

def f_x(n1, n2, x); 1.0 - fdist(n1, n2, x); end

.fdist(n1, n2, f) ⇒ Object

F-distribution



431
 
# File 'lib/statistics2.rb', line 431

def fdist(n1, n2, f); 1.0 - q_f(n1, n2, f); end

.fX_(n1, n2, x) ⇒ Object

Returns the integral of F-distribution with n1 and n2 degrees of freedom over [0, x].



580
 
# File 'lib/statistics2.rb', line 580

def fX_(n1, n2, x); fdist(n1, n2, x); end

.metaclass ⇒ Object

Easy access to our singleton



17
 
# File 'lib/statistics2.rb', line 17

def self.metaclass; class << self; self; end; end

.normal___x(z) ⇒ Object

Returns the integral of normal distribution over [x, Infty).



493
 
# File 'lib/statistics2.rb', line 493

def normal___x(z); 1.0 - normaldist(z); end

.normal__X_(z) ⇒ Object

Returns the integral of normal distribution over [0, x].



490
 
# File 'lib/statistics2.rb', line 490

def normal__X_(z); normaldist(z) - 0.5; end

.normaldist(z) ⇒ Object

normal-distribution



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# File 'lib/statistics2.rb', line 154

def normaldist(z)
  p_nor(z)
end

.normalx__x(z) ⇒ Object

Returns the integral of normal distribution over (-Infty, -x] + [x, Infty).



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# File 'lib/statistics2.rb', line 496

def normalx__x(z); 2.0 - normaldist(z) * 2.0; end

.normalxXX_(z) ⇒ Object

Returns the integral of normal distribution over (-Infty, x].



487
 
# File 'lib/statistics2.rb', line 487

def normalxXX_(z); normaldist(z); end

.pchi2_x(n, y) ⇒ Object

Return the P-value of the corresponding integral.



532
 
# File 'lib/statistics2.rb', line 532

def pchi2_x(n, y); pchi2dist(n, 1.0 - y); end

.pchi2dist(n, y) ⇒ Object

Returns the P-value of chi2dist().



236
 
# File 'lib/statistics2.rb', line 236

def pchi2dist(n, y); pchi2(n, 1.0 - y); end

.pchi2X_(n, y) ⇒ Object

Return the P-value of the corresponding integral.



535
 
# File 'lib/statistics2.rb', line 535

def pchi2X_(n, y); pchi2dist(n, y); end

.pf_x(n1, n2, x) ⇒ Object

Return the P-value of the corresponding integral.



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# File 'lib/statistics2.rb', line 587

def pf_x(n1, n2, x); pfdist(n1, n2, 1.0 - x); end

.pfdist(n1, n2, y) ⇒ Object

inverse of F-distribution



434
 
# File 'lib/statistics2.rb', line 434

def pfdist(n1, n2, y); pf(1.0 - y, n1, n2); end

.pfX_(n1, n2, x) ⇒ Object

Return the P-value of the corresponding integral.



590
 
# File 'lib/statistics2.rb', line 590

def pfX_(n1, n2, x); pfdist(n1, n2, x); end

.pnormal___x(y) ⇒ Object

Return the P-value of the corresponding integral.



510
 
# File 'lib/statistics2.rb', line 510

def pnormal___x(y); pnormalxXX_(1.0 - y); end

.pnormal__X_(y) ⇒ Object

Return the P-value of the corresponding integral.



507
 
# File 'lib/statistics2.rb', line 507

def pnormal__X_(y); pnormalxXX_(y + 0.5); end

.pnormaldist(y) ⇒ Object

inverse of normal-distribution



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# File 'lib/statistics2.rb', line 159

def pnormaldist(y)
  pnorm(y)
end

.pnormalx__x(y) ⇒ Object

Return the P-value of the corresponding integral.



513
 
# File 'lib/statistics2.rb', line 513

def pnormalx__x(y); pnormalxXX_(1.0 - y/2.0); end

.pnormalxXX_(z) ⇒ Object

Return the P-value of the corresponding integral.



504
 
# File 'lib/statistics2.rb', line 504

def pnormalxXX_(z); pnormaldist(z); end

.poisson_x(m, x) ⇒ Object 



730
 
# File 'ext/statistics2.c', line 730

def poisson_x(m, x); 1.0 - poissondist(m, x-1); end

.poissondens(m, x) ⇒ Object 



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# File 'ext/statistics2.c', line 737

def poissondens(m, x)
  return 0.0 if x < 0
  m = m.to_f
  m ** x * Math::E ** (-m) / perm(x)
end

.poissondist(m, x) ⇒ Object 



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# File 'ext/statistics2.c', line 744

def poissondist(m, x)
  (0..x).inject(0.0) do |s, k|
    s + poissondens(m, k)
  end
end

.poissonX_(m, x) ⇒ Object 



751
 
# File 'ext/statistics2.c', line 751

def poissonX_(m, x); poissondist(m, x); end

.pt___x(n, y) ⇒ Object

Return the P-value of the corresponding integral.



569
 
# File 'lib/statistics2.rb', line 569

def pt___x(n, y); ptdist(n, 1.0 - y); end

.pt__X_(n, y) ⇒ Object

Return the P-value of the corresponding integral.



566
 
# File 'lib/statistics2.rb', line 566

def pt__X_(n, y); ptdist(n, 0.5 + y); end

.ptdist(n, y) ⇒ Object

inverse of t-distribution



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# File 'lib/statistics2.rb', line 324

def ptdist(n, y)
  if y > 0.5
    pt(2.0 - y*2.0, n)
  else
    - pt(y*2.0, n)
  end
end

.ptx__x(n, y) ⇒ Object

Return the P-value of the corresponding integral.



560
 
# File 'lib/statistics2.rb', line 560

def ptx__x(n, y); ptdist(n, 1.0 - y / 2.0); end

.ptxXX_(n, y) ⇒ Object

Return the P-value of the corresponding integral.



563
 
# File 'lib/statistics2.rb', line 563

def ptxXX_(n, y); ptdist(n, y); end

.t___x(n, x) ⇒ Object

Returns the integral of t-distribution with n degrees of freedom over [x, Infty).



552
 
# File 'lib/statistics2.rb', line 552

def t___x(n, x); 1.0 - tdist(n, x); end

.t__X_(n, x) ⇒ Object

Returns the integral of t-distribution with n degrees of freedom over [0, x].



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# File 'lib/statistics2.rb', line 549

def t__X_(n, x); tdist(n, x) - 0.5; end

.tdist(n, t) ⇒ Object

t-distribution



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# File 'lib/statistics2.rb', line 321

def tdist(n, t); p_t(n, t); end

.tx__x(n, x) ⇒ Object

Returns the integral of normal distribution with n degrees of freedom over (-Infty, -x] + [x, Infty).



543
 
# File 'lib/statistics2.rb', line 543

def tx__x(n, x); 2.0 - tdist(n, x) * 2.0; end

.txXX_(n, x) ⇒ Object

Returns the integral of t-distribution with n degrees of freedom over (-Infty, x].



546
 
# File 'lib/statistics2.rb', line 546

def txXX_(n, x); tdist(n, x); end